A method of modeling an integrated circuit includes: specifying a layout for the integrated circuit, wherein the layout includes a plurality of devices arranged in a plurality of layers and a plurality of connections between the layers; specifying locations for a source point and an observation point for the integrated circuit; determining a plurality of static images for the source point and the observation point; determining a plurality of discrete complex images for the source point and the observation point; determining a Green's-function value for the source point and the observation point by combining the static images and the discrete complex images; and saving at least some values based on the Green's-function value.
Legal claims defining the scope of protection, as filed with the USPTO.
1. A method of modeling an integrated circuit, comprising: specifying a layout for the integrated circuit, wherein the layout includes a plurality of devices arranged in a plurality of layers and a plurality of connections between the layers; specifying locations for a source point and an observation point for the integrated circuit; determining a plurality of static images for the source point and the observation point; determining a plurality of discrete complex images for the source point and the observation point; using a computer for determining a Green's-function value for the source point and the observation point by combining the static images and the discrete complex images; and saving at least some values based on the Green's-function value.
2. The method of claim 1 , wherein specifying the layout includes specifying geometrical and electromagnetic parameters for at least some of the devices.
3. The method of claim 1 , wherein the devices are embedded in dielectric material included in the layers and include interconnects for making electrical connections between devices, and the connections between the layers include vias for making electrical connections between the layers.
4. The method of claim 1 , wherein the devices include interconnects for making electrical connections between devices, and the source point corresponds to one of the interconnects and the observation point corresponds to another of the interconnects.
5. The method of claim 1 , wherein the source point corresponds to a circuit input and the observation point corresponds to a circuit output, and the circuit input and the circuit output each include a voltage value or a current value from a transmission line model for the integrated circuit.
6. The method of claim 1 , wherein determining the static images includes determining magnitudes and distances for the static images in correspondence to the source point and the observation point.
7. The method of claim 1 , wherein determining the static images includes tracing a plurality of waves between the source point and the observation point, and at least some waves determine magnitudes and distances for the static images.
8. The method of claim 1 , wherein determining the discrete complex images includes: determining a truncation value for integrating a shifted Green's function that corresponds to a subtraction of the static images from the Green's function; and sampling the shifted Green's function on a path that is truncated by the truncation value to determine values for the discrete complex images.
9. The method of claim 8 , wherein determining the values for the discrete complex images includes: representing the shifted Green's function as a generalized pencil of functions to determine coefficients and exponents for the discrete complex images.
10. The method of claim 1 , wherein determining the Green's-function value includes: adding a contribution from the shifted Green's function to a contribution from the static images.
11. The method of claim 1 , wherein saving at least some values based on the Green's-function value includes storing the Green's-function value in a matrix that includes related Green's-function values for relating voltage values and current values in the integrated circuit.
12. The method of claim 1 , wherein the static images characterize a static portion of the Green's function for small frequencies of a spectral kernel for the Green's function.
13. The method of claim 1 , wherein determining the static images includes: tracing a plurality of waves between the source point and the observation point, wherein tracing the waves includes prioritizing the waves for tracing according to corresponding distances between the source point and the observation point so that waves with smaller distances have higher priorities, and calculating the static images from magnitudes and distances of the waves.
14. The method of claim 1 , wherein determining the static images includes: tracing a plurality of waves between the source point and the observation point by splitting waves into reflected and transmitted waves at one or more interfaces of the layers, wherein the source point and the observation point are in different layers of the integrated circuit, and calculating the static images from magnitudes and distances of the waves.
15. The method of claim 1 , wherein determining the static images includes: tracing a plurality of waves between the source point and the observation point by splitting waves into reflected and transmitted waves at one or more interfaces of the layers, wherein the source point and the observation point are in different layers of the integrated circuit, and calculating the static images from magnitudes and distances of the waves, determining the discrete complex images includes: determining a truncation value for integrating a shifted Green's function that corresponds to a subtraction of the static images from the Green's function, and sampling the shifted Green's function on a path based on the truncation value to determine values for the discrete complex images; and determining the Green's-function value includes: adding a contribution from the shifted Green's function to a contribution from the static images.
16. A computer-readable medium that stores a computer program that causes a computer to execute instructions for modeling an integrated circuit, wherein the computer program includes instructions for: specifying a layout for the integrated circuit, wherein the layout includes a plurality of devices arranged in a plurality of layers and a plurality of connections between the layers; specifying locations for a source point and an observation point for the integrated circuit; determining a plurality of static images for the source point and the observation point; determining a plurality of discrete complex images for the source point and the observation point; determining a Green's-function value for the source point and the observation point by combining the static images and the discrete complex images; and saving at least some values based on the Green's-function value.
17. The computer-readable medium of claim 16 , wherein specifying the layout includes specifying geometrical and electromagnetic parameters for at least some of the devices.
18. The computer-readable medium of claim 16 , wherein the devices are embedded in dielectric material included in the layers and include interconnects for making electrical connections between devices, and the connections between the layers include vias for making electrical connections between the layers.
19. The computer-readable medium of claim 16 , wherein the devices include interconnects for making electrical connections between devices, and the source point corresponds to one of the interconnects and the observation point corresponds to another of the interconnects.
20. The computer-readable medium of claim 16 , wherein the source point corresponds to a circuit input and the observation point corresponds to a circuit output, and the circuit input and the circuit output each include a voltage value or a current value from a transmission line model for the integrated circuit.
21. The computer-readable medium of claim 16 , wherein determining the static images includes determining magnitudes and distances for the static images in correspondence to the source point and the observation point.
22. The computer-readable medium of claim 16 , wherein determining the static images includes tracing a plurality of waves between the source point and the observation point, and at least some waves determine magnitudes and distances for the static images.
23. The computer-readable medium of claim 16 , wherein determining the discrete complex images includes: determining a truncation value for integrating a shifted Green's function that corresponds to a subtraction of the static images from the Green's function; and sampling the shifted Green's function on a path that is truncated by the truncation value to determine values for the discrete complex images.
24. The computer-readable medium of claim 23 , wherein determining the values for the discrete complex images includes: representing the shifted Green's function as a generalized pencil of functions to determine coefficients and exponents for the discrete complex images.
25. The computer-readable medium of claim 16 , wherein determining the Green's-function value includes: adding a contribution from the shifted Green's function to a contribution from the static images.
26. The computer-readable medium of claim 16 , wherein saving at least some values based on the Green's-function value includes storing the Green's-function value in a matrix that includes related Green's-function values for relating voltage values and current values in the integrated circuit.
27. An apparatus for modeling an integrated circuit, the apparatus comprising a computer for executing computer instructions, wherein the computer includes computer instructions for: specifying a layout for the integrated circuit, wherein the layout includes a plurality of devices arranged in a plurality of layers and a plurality of connections between the layers; specifying locations for a source point and an observation point for the integrated circuit; determining a plurality of static images for the source point and the observation point; determining a plurality of discrete complex images for the source point and the observation point; determining a Green's-function value for the source point and the observation point by combining the static images and the discrete complex images; and saving at least some values based on the Green's-function value.
28. The apparatus of claim 27 , wherein the computer includes a processor with memory for executing at least some of the computer instructions.
29. The apparatus of claim 27 , wherein the computer includes circuitry for executing at least some of the computer instructions.
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March 16, 2007
March 30, 2010
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